Non-homogeneous analysis of rogue wave probability evolution over a shoal

Abstract

Non-equilibrium evolution of wave fields, as occurring over sudden bathymetry variations, can produce rogue seas with anomalous wave statistics. We handle this process by modifying the Rayleigh distribution through the energetics of second-order theory and a non-homogeneous reformulation of the Khintchine theorem. The resulting probability model reproduces the enhanced tail of the probability distribution of unidirectional wave tank experiments. It also describes why the peak of rogue wave probability appears atop the shoal, and explains the influence of depth on variations in peak intensity. Furthermore, we interpret rogue wave likelihoods in finite depth through the $H$ – $\sigma$ diagram, allowing a quick prediction for the effects of rapid depth change apart from the probability distribution.

Enhanced extreme wave statistics of irregular waves due to accelerating following current over a submerged bar

“…The saturation depth has been indicated (without defining a terminology) in the theoretical work of Mendes et al. (2022), where those authors consider the enhancement of and takes place for . Yet, such a saturation depth has never been reported in experimental works.…”

“…2021 a , c ), or by the stochastic model for non-homogeneous processes introduced in Mendes et al. (2022).…”

“…For out-of-equilibrium sea states, the wave kinematics (Lawrence, Trulsen & Gramstad 2021;Zhang & Benoit 2021) as well as the sea-state equilibration process on a long spatial scale (Zhang et al 2019(Zhang et al , 2022 have been studied. From a theoretical perspective, the intensified freak wave probability provoked by significant depth variations could be described by the stochastic model of Li et al (2021b) which is built based on the second-order deterministic model (Li et al 2021a,c), or by the stochastic model for non-homogeneous processes introduced in Mendes et al (2022).…”

Saturation of rogue wave amplification over steep shoals

“…However, the homogeneity of surface waves is often assumed [27], whereas the relaxation of this condition is expected to play a role in rogue wave formation over a shoal [28]. Indeed, we recently provided a third framework [29] by taking nonhomogeneity into account. These three frameworks are complementary, because they rely on different physical approaches, respectively: Fluid dynamics analysis of wave harmonics, the statistical mechanics of water waves, and the lifting of long-held implicit assumptions regarding the homogeneity of ocean waves.…”

Novel methods for coupled prediction of extreme wind speeds and wave heights

“…In addition, spectrum bandwidth seems to have different types of effects in extreme wave distribution depending on whether they are in deep [25][26][27][28] or shallow water 13 . Furthermore, ocean processes such as shoaling or wave-current systems that drive wave trains out of equilibrium have been experimentally 22,25,[29][30][31][32][33][34][35][36][37] associated with increasing the occurrence of extreme waves by order of magnitude. However, it has been recently found that no established theoretical distribution to date, neither universal as Gumbel nor based on physical principles, can describe extreme wave statistics in a wide range of conditions .…”